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Let ab=1ab=1ab=1 and define
P=aa+1+bb+1 and Q=1a+1+1b+1. P=\frac{a}{a+1}+\frac{b}{b+1}\quad \text{ and }\quad Q=\frac{1}{a+1}+\frac{1}{b+1}.P=a+1a+b+1b and Q=a+11+b+11.
What can we say about PPP and Q?Q?Q?
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